HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 394 · 40 questions

The method (LCM or HCF?): Bells, lights, runners “together again”: find the LCM of the gaps. Biggest can, rope piece or tile that fits exactly: find the HCF. Leaves the same remainder r every time: LCM + r. Number of tiles = (length ÷ tile side) × (width ÷ tile side).

1. 1.A hall floor is 150 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
2. 2.Three temple bells ring every 10, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
3. 3.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 5.
4. 4.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 9 or 12.
5. 5.Zoya takes 30 seconds and Aarav takes 50 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
6. 6.Three temple bells ring every 4, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
7. 7.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 12 or 6.
8. 8.A hall floor is 315 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
9. 9.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 5, 12 or 10.
10. 10.Two tanks hold 50 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
11. 11.Two tanks hold 20 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
12. 12.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 9, 12 or 4.
13. 13.Arjun takes 40 seconds and Manav takes 45 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
14. 14.Three temple bells ring every 12, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
15. 15.Zoya takes 50 seconds and Ishaan takes 45 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
16. 16.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 9, 10 or 15.
17. 17.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 8, 6 or 4.
18. 18.Pooja takes 75 seconds and Zoya takes 40 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
19. 19.Diya takes 80 seconds and Karan takes 30 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
20. 20.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 8 or 5.
21. 21.Two tanks hold 140 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
22. 22.Three temple bells ring every 24, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
23. 23.A hall floor is 320 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
24. 24.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
25. 25.Two tanks hold 280 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
26. 26.Two tanks hold 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
27. 27.Three temple bells ring every 4, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
28. 28.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 9, 8 or 12.
29. 29.Three temple bells ring every 4, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
30. 30.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 9, 10 or 12.
31. 31.Manav takes 60 seconds and Farhan takes 50 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
32. 32.Two tanks hold 315 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
33. 33.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
34. 34.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
35. 35.Two tanks hold 140 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
36. 36.Three temple bells ring every 8, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
37. 37.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
38. 38.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 4 or 3.
39. 39.Three temple bells ring every 4, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
40. 40.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 5.

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